令e^x=t则原式=∫arctant/t*1/tdt=∫arctant/t^2dt=-∫arctantd(1/t)=-arctant/t+∫1/t*1/(t^2+1)dt=-arctant/t+∫(1/t-t/(t^2+1))dt=-arctant/t+∫dt/t-1/2∫d(t^2+1)/(t^2+1)=-arctant/t+ln|t|-1/2ln|t^2+1|+C=-ar...